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3 years ago

11

Brent counted 10 red cards, 10 black cards, and 20 blue cards in a deck of cards. What is the ratio of red cards to other cards?

Answers: A) 1:1 B) 1:2 C) 2:1 D) 1:3

1 answer:

Dmitrij [34]3 years ago

8 0

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

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What type of conic is given by the equation 4x^2+9y^2=36

zvonat [6]

Answer:

This is equation of ellipse

Step-by-step explanation:

we are given

$4x^2+9y^2=36$

We can see that right side is 36

so, we can make right side as 1 by dividing both sides by 36

$\frac{4x^2+9y^2}{36} =\frac{36}{36}$

$\frac{4x^2+9y^2}{36} =1$

$\frac{4x^2}{36}+\frac{9y^2}{36} =1$

we can simplify it

$\frac{x^2}{9}+\frac{y^2}{4} =1$

we can rewrite it as

$\frac{x^2}{3^2}+\frac{y^2}{2^2} =1$

now, we can compare it with standard equation of ellipse

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} =1$

we can see that both equations are similar

so, this is equation of ellipse

8 0

2 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

3 years ago

Cuanto es 32256 dividido para 25 con proceso

Bond [772]

Answer:

49905 dividido por 81 = 616.11

32256 dividido por 25= 1290.24

58308 dividido por 64= 911.06

9218 dividido por 768= 12.0026.

4 0

3 years ago

Is the formula s=(n-2)180

Phantasy [73]

Answer:

Number of sides of the polygon

Step-by-step explanation:

The formula $S=(n-2)180$ is the sum of the measures of interior angles. So that's what S stands for. The only other variable remaining is n which is the number of sides of the polygon.

There's nothing I can do to help you understand this, you just have to memorize it.

5 0

2 years ago

Which are true about the pyramid? Check all that apply.

Travka [436]

The statements that are true about the pyramid are

The base of the pyramid is a square with four sides, each measuring 756 feet.

The slant height of the pyramid is 612 feet.

All four triangular faces are congruent.

The pyramid has four lateral faces.

<h3>Properties of a Square pyramid </h3>

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

The length of a side of its base is 756 ft

and

The height / altitude of a triangular face is 612 ft

Since the pyramid is a square pyramid,

Then, the base must be a square with each side measuring 756 feet

∴ The first statement is true

Since the height of a triangular face is 612 ft,

Then,

∴ The slant height of the pyramid is 612 feet

NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face

Thus, the second statement is true

Since the triangular faces each have a base of 756ft and a height of 612 ft,

Then,

All four triangular faces are congruent

∴ The fourth statement is true

NOTE: Lateral sides of a solid are the faces on the <u>sides</u> of the shape

The pyramid has four lateral faces which are each a triangle

∴ The last statement is true

Hence, the statements that are true about the pyramid are

The base of the pyramid is a square with four sides, each measuring 756 feet.

The slant height of the pyramid is 612 feet.

All four triangular faces are congruent.

The pyramid has four lateral faces.

Learn more on Pyramid here: brainly.com/question/10042135

#SPJ1

4 0

2 years ago